As a thought experiment, suppose I modified the value of $c$ (speed of light) in some local region and attempted to measure it with a clock placed in that same region. I will denote this new unmeasured speed $c'$. If I tried to measure $c'$ with a clock then (based on my understanding of physics) I would still arrive at the conclusion that $c=c'$ since the rate at which physical processes evolve in a region is dependent on the value of light-speed in that region. Consequently the rate at which the internal processes of a clock evolve will be dependent on the value of light-speed as well. This will effectively change the way I measure $c'$ and cancel out any measurable $\Delta c$.
Based on my reasoning above, I feel it is necessary to ask...
1.) What do exactly do cosmologists mean when they assert that the inflationary period was a period where the speed of light was different than what we measure it to be today?
2.) How do cosmologists define a value of light-speed which is different from our current value?
3.) How could a cosmologist measure a value of the speed of light which is different from its current value?
4.) Were is my logic flawed?
I understand they did this because it could explain the isotropic nature of the physical characteristics space-like separating events; that is, I understand why they did it just not how they model it theoretically.